WASHINGTON (Reuters) - The White House and congressional Republicans blasted each other on Tuesday over equal pay in a battle for women's votes as Democrats try to hold the U.S. Senate in the November midterm elections.

President Barack Obama signed an executive order prohibiting federal contractors from retaliating against employees for disclosing pay levels to co-workers and attacked Republicans for opposing broader legislation that would make the practice illegal for companies nationwide.

Republicans said pay discrimination was already illegal and predicted the Democrat-supported Paycheck Fairness Act would prompt frivolous lawsuits and discourage companies from hiring.

The Democratic-led Senate is set to hold a procedural vote on the measure on Wednesday but even if the legislation clears that chamber, the Republican-dominated House of Representatives appears likely to oppose it.

The dispute underscored the importance that both parties place on women voters in an election year where Democrats fear losing control of the Senate and Republicans are seeking to defend their dominance in the House of Representatives.

"I don't know why you would resist the idea that women should be paid the same as men, and then deny that that's not always happening out there," Obama said at the White House at an East Room event filled with women.

"If Republicans in Congress want to prove me wrong, if they want to show that they, in fact, do care about women being paid the same as men, then show me. They can start tomorrow. They can join us in this, the 21st century, and vote yes on the Paycheck Fairness Act."

Obama cited U.S. Census data that show the average full-time female worker earned 77 cents for every dollar a man earns. The U.S. Department of Labor says the gap is tighter, with women in full-time jobs earning 81 cents for every dollar men earn.

Critics, including the U.S. Chamber of Commerce, a business lobby group, say both figures are misleading.

Other factors also affect the data, such as types of jobs worked by women, hours worked, and college majors, which affect whether people get higher- or lower-paying jobs, said Andrew Biggs, a resident scholar at the American Enterprise Institute.

"The idea that there's a 23 percent pay gap between men and women based on discrimination is flat-out false," he said.

The Republican National Committee accused Obama's party of playing politics.

"These are the same Democrats who controlled the White House and Senate for the last five years but always seem to wait for an election year to push another empty promise," the RNC said in a memo distributed to reporters.

"The truth is the 'Paycheck Fairness Act' is a desperate political ploy. And Democrats are cynically betting that Americans aren't smart enough to know better."

RETALIATION

Support from women helped propel Obama to the White House in 2008 and 2012, and the president frequently recalls that the first bill he signed into law was the Lilly Ledbetter Fair Pay Act, which extended time periods for employees to file claims for wages lost as a result of discrimination.

Lilly Ledbetter, who fought for back pay after discovering she had been paid less than her male colleagues for doing the same job, joined Obama at the event.

Focus on the issue put a spotlight on White House practices, however, and Obama's chief spokesman Jay Carney was forced to address data showing a pay gap between men and women working there. Carney said men and women with the same White House positions made equal pay.

The White House said Obama's executive order would encourage transparency by allowing employees of federal contractors to compare notes on their pay, discover violations and seek corrective action.

Obama also directed the U.S. secretary of labor to create regulations that require federal contractors to submit to the government summary data on employee compensation including details on gender and race and use that to encourage voluntary compliance with equal pay laws.

"We know that about half of all workers report that discussion of wages and salary information is either discouraged or prohibited, and/or could lead to punishment," said Betsey Stevenson, a member of the White House Council of Economic Advisers, in a conference call with reporters on Monday.

"So a lot of workers work under the threat that this could affect their job, this could cost them their job."

The Paycheck Fairness Act would require employers to show that any pay disparity between men and women is not gender-based. AEI's Biggs said that would force employers to prove a negative.